Well...they did.

​

Just its structure was different.

See, Comintern was established to spread Communism globally. Stalin pulled the plug on it in 1943, to avoid exacerbating the West, as their relationship was on a diplomatic tightrope. He later established the Cominform aka the Warsaw Pact (Warszavski Dogovor). WP succeded Cominform, as Khruschev later dissovled it too, in a bid of reforms.